The new Blaugrana trainer is confident the South American trio will form a dangerous attack and has made it clear Xavi and Dani Alves still have a future at the club.
Club icon Johan Cruyff recently criticized Barcelona over the signing of Suarez, yet Enrique believes the former Liverpool star will prove to be a valuable addition.
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"Every coach wants to have the best players. I am delighted to have all three of Messi, Neymar and Suarez. The more great players, the better," Luis Enrique said at a press conference. "I am always looking to get the best out of my players and that includes Messi. Some players occasionally go through a difficult period, but you can always rely on Messi. He did some fantastic things for Argentina at the World Cup and is still the best player in the world for me. He's an example to follow for many players.
"We will try and make a team which isn't predictable, staying true to the essence of this club. We want to be able to use different concepts and tactics and to surprise the opponent. It's not about two or three players, but about the team as a whole. But of course, a signing like Suarez helps you put together a great team."
Enrique then went on to stress that Xavi and Dani Alves still have a role to play at Barcelona if it is up to him, before adding that he's keen to sign a new central defender.
"I have talked with Xavi about his future. He still has a contract here. But it's up to him to make a decision," he said. "Dani Alves has an ongoing contract with Barcelona. We'll talk and see what he has in mind and we'll explain our plans as well.
"Our main priority now is to sign a center back. We'll see what he can give the team once we've sorted that."